Here are the essential concepts you must grasp in order to answer the question correctly.
Composition of Functions
The composition of functions involves combining two functions to create a new function. If you have two functions, f(x) and g(x), the composition is denoted as (f ∘ g)(x) = f(g(x)). This means you first apply g to x, and then apply f to the result of g. Understanding this concept is crucial for manipulating and evaluating complex functions.
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Function Notation
Function notation is a way to represent functions mathematically, typically using symbols like f(x) to denote the output of a function f for a given input x. This notation allows for clear communication of mathematical ideas and operations involving functions, making it easier to work with compositions and transformations of functions.
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Evaluating Functions
Evaluating functions involves substituting a specific value into a function to find the corresponding output. For example, if f(x) = 2x + 3, evaluating f(2) would yield 2(2) + 3 = 7. This skill is essential for working with composed functions, as it requires substituting values into multiple functions in sequence.
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